全一卷
1.-5的绝对值等于( )
A.-5 | B.5 | C.![]() | D.![]() |
2.下面计算正确的是( )
A.![]() | B.![]() |
C.![]() | D.![]() |
3.如图所示,该几何体的俯视图为( )
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A.![]() | B.![]() | C.![]() | D.![]() |
4.在函数
中,自变量
的取值范围是( )
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A.![]() | B.![]() | C.![]() | D.![]() |
5.四张背面完全相同的卡片,正面分别印有等腰三角形、圆、平行四边形、正六边形,现在把它们的正面向下,随机的摆放在桌面上,从中任意抽出一张,则抽到的卡片正面是中心对称图形的概率是( )
A.![]() | B.![]() | C.![]() | D.1 |
6.如图,
是
的角平分线,过点
作
交
延长线于点
,若
,
,则
的度数为( )
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A.100° | B.110° | C.125° | D.135° |
7.如图,在四边形
中,
,
,
,
,分别以
和
为圆心,以大于
的长为半径作弧,两弧相交于点
和
,直线
与
延长线交于点
,连接
,则
的内切圆半径是( )
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A.4 | B.![]() | C.2 | D.![]() |
8.如图,二次函数
(
)的图象与
轴交于
,
两点,与
轴交于点
,点
坐标为
,点
在
与
之间(不包括这两点),抛物线的顶点为
,对称轴为直线
,有以下结论:①
;②若点
,点
是函数图象上的两点,则
;③
;④
可以是等腰直角三形.其中正确的有( )
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A.1个 | B.2个 | C.3个 | D.4个 |
9.据有关报道,2020年某市斥资约5 800 000元改造老旧小区,数据5 800 000科学记数法表示为_________ .
10.因式分解:
_________ .
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11.一次函数
,且
,则它的图象不经过第_________ 象限.
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12.甲、乙两人进行飞镖比赛,每人投5次,所得平均环数相等,其中甲所得环数的方差为5,乙所得环数如下:2,3,5,7,8,那么成绩较稳定的是_________ (填“甲”或“乙”).
13.关于
的方程
有两个实数根,则
的取值范围是_________ .
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14.如图,矩形
的边
在
轴上,点
在反比例函数
的图象上,点
在反比例函数
的图象上,若
,
,则
_________ .
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15.如图,在四边形
中,
,
,
,
,点
和点
分别是
和
的中点,连接
,
,
,若
,则
的面积是_________ .
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16.如图,在矩形
中,
,
,连接
,以
为边,作矩形
使
,连接
交
于点
;以
为边,作矩形
,使
,连接
交
于点
;以
为边,作矩形
,使
,连接
交
于点
;…按照这个规律进行下去,则
的面积为_________.
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17.先化简,再求代数式的值:
,其中
.
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18.如图,在平面直角坐标系中,网格的每个小方格都是边长为1个单位长度的正方形,点
,
,
的坐标分别为
,
,
,先以原点
为位似中心在第三象限内画一个
,使它与
位似,且相似比为2:1,然后再把
绕原点
逆时针旋转90°得到
.
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(1)画出
,并直接写出点
的坐标;
(2)画出
,直接写出在旋转过程中,点
到点
所经过的路径长.
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(1)画出
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(2)画出
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19.某校为了解疫情期间学生居家学习情况,以问卷调查的形式随机调查了部分学生居家学习的主要方式(每名学生只选最主要的一种),并将调查结果绘制成如下不完整的统计图.
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根据以上信息回答下列问题:
(1)参与本次问卷调查的学生共有_________人,其中选择
类型的有_________人;
(2)在扇形统计图中,求
所对应的圆心角度数,并补全条形统计图;
(3)该校学生人数为1250人,选择
、
、
三种学习方式大约共有多少人?
种类 | |||||
学习方式 | 老师直播 教学课程 | 国家教育云平台 教学课程 | 电视台播放 教学课程 | 第三方 网上课程 | 其他 |
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根据以上信息回答下列问题:
(1)参与本次问卷调查的学生共有_________人,其中选择
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(2)在扇形统计图中,求
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(3)该校学生人数为1250人,选择
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20.在一个不透明的口袋中装有4个依次写有数字1,2,3,4的小球,它们除数字外都相同,每次摸球前都将小球摇匀.
(1)从中随机摸出一个小球,小球上写的数字不大于3的概率是_________;
(2)若从中随机摸出一球不放回,再随机摸出一球,请用画树状图或列表的方法,求两次摸出小球上的数字和 恰好是偶数的概率.
(1)从中随机摸出一个小球,小球上写的数字不大于3的概率是_________;
(2)若从中随机摸出一球不放回,再随机摸出一球,请用画树状图或列表的方法,求两次摸出小球上的
21.为帮助贫困山区孩子学习,某学校号召学生自愿捐书,已知七、八年级同学捐书总数都是1800本,八年级捐书人数比七年级多150人,七年级人均捐书数量是八年级人均捐书数量的1.5倍,求八年级捐书人数是多少?
22.如图,已知
,以
为直径的
交
于点
,连接
,
的平分线交
于点
,交
于点
,且
.
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(1)判断
所在直线与
的位置关系,并说明理由;
(2)若
,
,求
的半径.
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(1)判断
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(2)若
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23.如图,小岛
和
都在码头
的正北方向上,它们之间距离为
,一艘渔船自西向东匀速航行,行驶到位于码头
的正西方向
处时,测得
,渔船速度为
,经过
,渔船行驶到了
处,测得
,求渔船在
处时距离码头
有多远?(结果精确到
)
(参考数据:
,
,
,
,
,
)
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(参考数据:
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24.某服装批发市场销售一种衬衫,衬衫每件进货价为50元,规定每件售价不低于进货价,经市场调查,每月的销售量
(件)与每件的售价
(元)满足一次函数关系,部分数据如下表:
(1)求出
与
之间的函数表达式;(不需要求自变量
的取值范围)
(2)该批发市场每月想从这种衬衫销售中获利24000元,又想尽量给客户实惠,该如何给这种衬衫定价?
(3)物价部门规定,该衬衫的每件利润不允许高于进货价的30%,设这种衬衫每月的总利润为
(元),那么售价定为多少元可获得最大利润?最大利润是多少?
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售价 | 60 | 65 | 70 |
销售量 | 1400 | 1300 | 1200 |
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(2)该批发市场每月想从这种衬衫销售中获利24000元,又想尽量给客户实惠,该如何给这种衬衫定价?
(3)物价部门规定,该衬衫的每件利润不允许高于进货价的30%,设这种衬衫每月的总利润为
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25.已知:菱形
和菱形
,
,起始位置点
在边
上,点
在
所在直线上,点
在点
的右侧,点
在点
的右侧,连接
和
,将菱形
以
为旋转中心逆时针旋转
角(
).
(1)如图1,若点
与
重合,且
,求证:
;
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(2)若点
与
不重合,
是
上一点,当
时,连接
和
,
和
所在直线相交于点
;
①如图2,当
时,请猜想线段
和线段
的数量关系及
的度数;
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②如图3,当
时,请求出线段
和线段
的数量关系及
的度数;
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③在②的条件下,若点
与
的中点重合,
,
,在整个旋转过程中,当点
与点
重合时,请直接写出线段
的长.
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(1)如图1,若点
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(2)若点
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①如图2,当
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②如图3,当
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③在②的条件下,若点
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26.如图1,在平面直角坐标系中,抛物线
与
轴交于
,
两点,
点坐标为
,与
轴交于点
,直线
与抛物线交于
,
两点.
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(1)求抛物线的函数表达式;
(2)求
的值和
点坐标;
(3)点
是直线
上方抛物线上的动点,过点
作
轴的垂线,垂足为
,交直线
于点
,过点
作
轴的平行线,交
于点
,当
是线段
的三等分点时,求
点坐标;
(4)如图2,
是
轴上一点,其坐标为
,动点
从
出发,沿
轴正方向以每秒5个单位的速度运动,设
的运动时间为
(
),连接
,过
作
于点
,以
所在直线为对称轴,线段
经轴对称变换后的图形为
,点
在运动过程中,线段
的位置也随之变化,请直接写出运动过程中线段
与抛物线有公共点时
的取值范围.
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(1)求抛物线的函数表达式;
(2)求
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(3)点
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(4)如图2,
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